Solve |2x -5| =x +2

Question

Solve the equation

x_{1} = 1, x_{2} = 7

Evaluate

∣ 2 x - 5 ∣ = x + 2

Rewrite the expression

∣ 2 x - 5 ∣ - x - 2 = 0

Separate the equation into 2 possible cases

2 x - 5 - x - 2 = 0, 2 x - 5 \geq 0 - (2 x - 5) - x - 2 = 0, 2 x - 5 < 0

Solve the equation

More Steps

Evaluate

2 x - 5 - x - 2 = 0

Calculate

More Steps

Evaluate

2 x - 5 - x - 2

Subtract the terms

x - 5 - 2

Subtract the numbers

x - 7

x - 7 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 7

Removing 0 doesn't change the value,so remove it from the expression

x = 7

x = 7, 2 x - 5 \geq 0 - (2 x - 5) - x - 2 = 0, 2 x - 5 < 0

Solve the inequality

More Steps

Evaluate

2 x - 5 \geq 0

Move the constant to the right side

2 x \geq 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

2 x \geq 5

Divide both sides

\frac{2 x}{2} \geq \frac{5}{2}

Divide the numbers

x \geq \frac{5}{2}

x = 7, x \geq \frac{5}{2} - (2 x - 5) - x - 2 = 0, 2 x - 5 < 0

Solve the equation

More Steps

Evaluate

- (2 x - 5) - x - 2 = 0

Calculate

- 2 x + 5 - x - 2 = 0

Calculate the sum or difference

More Steps

Evaluate

- 2 x + 5 - x - 2

Subtract the terms

- 3 x + 5 - 2

Subtract the numbers

- 3 x + 3

- 3 x + 3 = 0

Move the constant to the right-hand side and change its sign

- 3 x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

- 3 x = - 3

Change the signs on both sides of the equation

3 x = 3

Divide both sides

\frac{3 x}{3} = \frac{3}{3}

Divide the numbers

x = \frac{3}{3}

Divide the numbers

More Steps

Evaluate

\frac{3}{3}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 7, x \geq \frac{5}{2} x = 1, 2 x - 5 < 0

Solve the inequality

More Steps

Evaluate

2 x - 5 < 0

Move the constant to the right side

2 x < 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

2 x < 5

Divide both sides

\frac{2 x}{2} < \frac{5}{2}

Divide the numbers

x < \frac{5}{2}

x = 7, x \geq \frac{5}{2} x = 1, x < \frac{5}{2}

Find the intersection

x = 7 x = 1, x < \frac{5}{2}

Find the intersection

x = 7 x = 1

Solution

x_{1} = 1, x_{2} = 7

Show Solution

Solve the equation

Graph